Find an integer n > 20 so that the equation 3x = b always have a unigue solution in Zn regardless of the value b

Not to sure what Zn means
Can the value of b be anything?

Please help

May 7th 2006, 11:07 AM

ThePerfectHacker

Quote:

Originally Posted by mathlg

Find an integer n > 20 so that the equation 3x = b always have a unigue solution in Zn regardless of the value b

Not to sure what Zn means
Can the value of b be anything?

Please help

By, we mean the group of positive integers added modulo .

I believe the theorem goes that, has a solution in when, .
For your problem you need to find all the integers relatively prime to and less. This is called the 'phi-function'. Thus, you need to find the smalles such as all the previous integers are relatively prime to it. Meaning a prime number, the smallest after 20 is 23.

May 7th 2006, 11:20 AM

mathlg

So you are saying that since n > 20 the next smallest prime number is 23. That would be the integer im looking for in the problem? I get confused when it says regardless of the value b.

May 7th 2006, 02:13 PM

ThePerfectHacker

Quote:

Originally Posted by mathlg

So you are saying that since n > 20 the next smallest prime number is 23. That would be the integer im looking for in the problem? I get confused when it says regardless of the value b.